An adaptive Newton-method based on a dynamical systems approach

Amrein, Mario; Wihler, Thomas (2014). An adaptive Newton-method based on a dynamical systems approach. Communications in Nonlinear Science and Numerical Simulation, 19(9), pp. 2958-2973. Elsevier 10.1016/j.cnsns.2014.02.010

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The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possible to interpret the Newton method as a discrete dynamical system and thereby to cast it in the framework of an adaptive step size control procedure. In so doing, our goal is to reduce the chaotic behavior of the original method without losing its quadratic convergence property close to the roots. The performance of the modified scheme is illustrated with various examples from algebraic and differential equations.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Amrein, Mario and Wihler, Thomas

Subjects:

500 Science > 510 Mathematics

ISSN:

1007-5704

Publisher:

Elsevier

Language:

English

Submitter:

Mario Amrein

Date Deposited:

24 Apr 2015 14:49

Last Modified:

07 Oct 2015 10:24

Publisher DOI:

10.1016/j.cnsns.2014.02.010

BORIS DOI:

10.7892/boris.67150

URI:

https://boris.unibe.ch/id/eprint/67150

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